Memory and anticipation: two main theorems for Markov regime-switching stochastic processes

被引：0
|
作者：
Savku, E. [1 ,2 ]
机构：
[1] Atilim Univ, Dept Comp Engn, TR-06836 Ankara, Turkiye
[2] Univ Oslo, Dept Math, Postboks 1053, N-0316 Oslo, Norway
来源：
STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES | 2024年
关键词：
Stochastic differential delay equations; anticipated backward stochastic differential equations; Regime-switches; MAXIMUM PRINCIPLE; DIFFERENTIAL-EQUATIONS; DELAY EQUATIONS; GAMES; JUMPS;
D O I：
10.1080/17442508.2024.2427733
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present two main theorems for stochastic processes with a Markov regime-switching model. First, we work on an existence-uniqueness theorem for a Stochastic Differential Delay Equation with Jumps and Regimes (SDDEJRs). Then we provide the duality between an SDDEJR and an Anticipated Backward Stochastic Differential Equation with Jumps and Regimes (ABSDEJRs). Our goal is to provide two technical and fundamental theorems for the future theoretical and applied developments of time-delayed and time-advanced models.
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页数：18
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